A comparison of weighted cyclic reciprocal sums

Proved

WorkbookSource.base_29330

by wamlart · Sep 13, 2026 · Mathlib 0df444a (Lean v4.33.1)

lean-workbooksource-checked

INEQUALITY I Let $a,b,c$ be positive real numbers.Prove that $\frac{1}{{a + 2b}} + \frac{1}{{b + 2c}} + \frac{1}{{c + 2a}} + \frac{3}{{a + b + c}} \ge 4\left( {\frac{1}{{3a + 2b + c}} + \frac{1}{{a + 3b + 2c}} + \frac{1}{{2a + b + 3c}}} \right).$

Source: InternLM Lean-Workbook, record lean_workbook_29330 (Apache-2.0). Complete source proposition preserved; proof developed independently.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.base_29330 (a b c : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) : 1 / (a + 2 * b) + 1 / (b + 2 * c) + 1 / (c + 2 * a) + 3 / (a + b + c) ≥ 4 * (1 / (3 * a + 2 * b + c) + 1 / (a + 3 * b + 2 * c) + 1 / (2 * a + b + 3 * c))  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_29330; Apache-2.0

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